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A376864 4-brilliant numbers with distinct prime factors.

%I A376864 #12 Oct 27 2024 16:09:02
%S A376864 210,46189,55913,62491,70499,75361,78793,81719,84227,89947,95381,
%T A376864 96577,99671,100529,101959,103037,104533,110143,111397,114257,116831,
%U A376864 121693,121771,124729,127699,128557,128843,130169,131461,133331,134849,139403,141427,143429
%N A376864 4-brilliant numbers with distinct prime factors.
%H A376864 Michael S. Branicky, <a href="/A376864/b376864.txt">Table of n, a(n) for n = 1..10000</a>
%e A376864 210 = 2*3*5*7 is a term.
%e A376864 130169 = 13*17*19*31 is a term.
%o A376864 (Python)
%o A376864 from sympy import factorint
%o A376864 def ok(n):
%o A376864     f = factorint(n)
%o A376864     return len(f) == sum(f.values()) == 4 and len(set([len(str(p)) for p in f])) == 1
%o A376864 print([k for k in range(144000) if ok(k)]) # _Michael S. Branicky_, Oct 08 2024
%o A376864 (Python)
%o A376864 from math import prod
%o A376864 from sympy import primerange
%o A376864 from itertools import count, combinations, islice
%o A376864 def bgen(d): # generator of terms that are products of d-digit primes
%o A376864     primes, out = list(primerange(10**(d-1), 10**d)), set()
%o A376864     for t in combinations(primes, 4): out.add(prod(t))
%o A376864     yield from sorted(out)
%o A376864 def agen(): # generator of terms
%o A376864     for d in count(1): yield from bgen(d)
%o A376864 print(list(islice(agen(), 34))) # _Michael S. Branicky_, Oct 08 2024
%Y A376864 Intersection of A046386 and A376704.
%K A376864 nonn,base,easy
%O A376864 1,1
%A A376864 _Paul Duckett_, Oct 07 2024
%E A376864 Terms corrected by _Michael S. Branicky_, Oct 08 2024